\newproblem{lay:2_1_24}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.1.24}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Suppose $A$ is a $n\times 3$ matrix whose columns span $\mathbb{R}^3$. Explain how to construct an $n\times 3$ matrix $D$ such that $AD=I_3$.
}{
  % Solution
	Let us define a generic matrix $D$
	\begin{center}
		$D=\begin{pmatrix} d_{11} & d_{12} & ... & d_{1n} \\ d_{21} & d_{22} & ... & d_{2n} \\ ... & ... & ... & ... \\ d_{m1} & d_{m2} & ... & d_{mn} \end{pmatrix}$
	\end{center}
	We need that $AD=I_3$. This gives us 9 ($=3\cdot 3$) equations to find the matrix $D$. If the columns of $A$ span $\mathbb{R}^3$ and $n>3$, the system 
	is compatible indeterminate and there will be infinite solutions to the problem. If $n=3$, there is a single solution to the problem. In the case that the columns
	of $A$ did not span $\mathbb{R}^3$, there would not be any solution to the problem.
}
\useproblem{lay:2_1_24}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
